I think most agree that FFVII and FFVIII were phenomenal games (and the games before them great for their time as well). I think the games that have come since are the most often debated. I'm going to offer my personal views on these games and a brief (and probably incomplete) analysis of the controversy over some of them.
FFIX: A lot of people hate this game. After the graphical genius of FFVII and FFVIII, this game's return to two-dimensional graphics turned a lot of people off. "The Crystal Comes Back," was the tagline I remember seeing on it and when I picked up the game, I expected only to see the traditional crystal(s) of the early SNES games and similar themes. I think this is where the disconnect is with so many people. They expected something else. It was meant to be a nostalgic throw-back to the older games (with references to Cloud and Squall, and others).
In my opinion, even if you were expecting the next growth in visuals, the story makes up for it. The story is complex and dramatic. The characters don't have single emotions. Sarah's attitudes toward Brahne aren't simply one-dimensional. She feels respect, hatred, confusion, disgust, remorse, regret, and even love for her (even after all that happens).
The other complaint I've heard is against the main character, Zidane. He's not the stoic or troubled Cloud, he's not the "badass" (and also troubled) Squall. He's aloof, boyish, and also troubled. Oddly, he catches flack from everyone more so because of his depression in Pandemonium and after losing Sarah than he does for being boyish (not "manly"). People sometimes make the same complaints about Cloud, but they somehow overlook them. So why don't they accept the fact that, after discovering he was manufactured to kill people, Zidane is a little shocked (I'm pretty sure I'd be shocked too).
FFX: This was a good game in my opinion. It was a little "sappy" at times, I suppose, but I thought the emotional "appeals" were good. Many of the complaints with this game were the same as with FFIX. People didn't like Zidane and they didn't like Tidus. Yet they ignored it when Cloud bitched out in FFVII.
My biggest complaint is with the ending (not the full motion videos). The battles were highly disappointing. You could become too powerful at such a rapid place once you unlocked the Omega Ruins by racing along the Sphere Grid. Sin went down far too easily. And Yu-Yevon was a joke. He died incredibly quickly and, to make matters even worse, you couldn't die. It was physically impossible. You had a permanent auto-life on during the battle.
So, if you ignore the horrible execution of the final battle and the rapid leveling pace at the end of the game, I'd say it's a good game (which I do).
It also had some fun and difficult mini-games and quests (the chocobo race was fun, if aggravating).
FFX-2: This was a fun game, but it shouldn't have existed to be honest. The story was alright (not amazing, but it filled in a lot about the history of the world, which I liked). But this broke the "no direct sequels" unofficial rule.
Also, I've heard a lot of complaints against the dresspheres. People complain that it's like a dress-up game or that it's stupid to have the characters change their "clothes" in mid-battle. To this I respond, what the hell has the job system been in previous games? Why do characters carry around 30 different "outfits" in Final Fantasy V to change into between battles to adopt new powers? It's a game. Besides, at least FFX-2 explained it to some degree with the spheres. FFV didn't do any such thing (not that I complain), and no one else minds, yet they whine about FFX-2.
The other complaint I've heard is that all the characters are female. Who cares? Does it really matter? Yuna obviously had to be the main character. Wakka and Lulu were obvious out of the picture. The same goes for Tidus and Auron and Kimahri. This leaves Rikku from FFX. So she comes along. After all, she's related to Yuna and she's an Al-Bhed and the Al-Bhed have been recovering machina like the airship. So it makes sense. Where does Paine fit in? Well, does it really matter if her Crimson Squad had a single female member? Are you seriously complaining that it wasn't four males? It could have been, sure, just as it could have been four females. So, get over it. Yes, the characters are female. It's not important.
Now, I will admit there are "silly" or even "stupid" parts in the game, and the massage section was hilarious at best and creepy at worst. Again, this game should not have existed, but it's not a bad game. If they had somehow made it work with FFX as one game (which would be difficult, but there have been character/party changes in other games before), then I wouldn't have minded it. I think it would have been hard to make it work though because shifting to two years later, a different combat system, et cetera would be a horrible transition that no game could successfully explain. So, this is a tragic situation. It couldn't be one game, but it shouldn't have been two games.
FFXI: This game annoys me to no end. It looks like a great game. I've heard from friends that play it that it's wonderful. But why the hell does it have a number? Final Fantasy Tactics didn't have a number and it's more related to the numbered games (FFXII, FFVII, FFX and FFX-2 (through FFVII)). This should have been called Final Fantasy: Online. It's not a console game. This is not part of the numbered series. I'm still waiting for FFXI to come out.
FFXII: This was SquareEnix's way of making a console game like an online RPG. They made massive maps, et cetera. I can't offer any good critique of the plot elements because I never got past the second mission because I got sick of spending 5 minutes getting across the city any time I wanted to go somewhere. I understand the desire for realism, but at some point, you're just playing real life and not a game. It's like Podcast 2 discussed (shameless plug for BrilliantGameologists), some things just don't make sense and you have to accept it because it's a game. You don't want to have to play out the characters going to the bathroom. I don't want to spend an hour walking across the City of Orange in a video game just because that's how long it takes in real life.
FFXII-2: I haven't played this. I'm not even positive it's been released yet, but I think it has. My complaint against this is the same as with FFX-2. Final Fantasy shouldn't about direct sequels, in my opinion.
FFXIII: What the hell is wrong with this game? It looks visually brilliant. The stories sound complex. Oh, right, that's the problem. It's not one game. It's three. They even say they aren't directly related. So why are they under the same number? Name them XIII, XIV, and XV and be done with it. Stop killing my childhood upbringing (yes, I was raised on Final Fantasy).
My next complaint is against the "Agito" game in this group. It's for cellular phones. Like FF: Online, it shouldn't have a number. The changes since the merge with Enix sicken me...
FFTA: This game is a joke in my opinion. The graphics are cartoon-ish. The story is weak (childish compared to the much more deep, layered, and complex dramas of most Final Fantasy games). It could have been much more serious than it was with the conflict of interests between Marche and Mewt. Also, who the hell is named Marche or Mewt, to make a serious inquiry? I honestly want an answer on that from somebody.
This game was shameful compared to FFT.
Offer your own opinions or perceptions about what you think the controversies are over.
Also, feel free to discuss the earlier games if it's relevant to this topic (Down the Drain?).